scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

Higher Order Convergent Newton Type Iterative Methods

2018 ◽  
Vol 1 (2) ◽  
pp. 32-39
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Numerical Methods ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Predictor Corrector ◽  
Appl Math

Newton method is one of the most widely used numerical methods for solving nonlinear equations. McDougall and Wotherspoon [Appl. Math. Lett., 29 (2014), 20-25] modified this method in predictor-corrector form and get an order of convergence 1+√2. More on the PDF

scholarly journals Why using symbolic computation for proving the convergence of iterative methods?

2013 ◽  
Vol 22 (2) ◽  
pp. 127-134
Author(s):  
GHEORGHE ARDELEAN ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Nonlinear Equations ◽  
Symbolic Computation ◽  
Newton’S Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Order Convergence ◽  
Convergence Error ◽  
Higher Order Convergence ◽  
Appl Math

In [YoonMe Ham et al., Some higher-order modifications of Newton’s method for solving nonlinear equations, J. Comput. Appl. Math., 222 (2008) 477–486], some higher-order modifications of Newton’s method for solving nonlinear equations are presented. In [Liang Fang et al., Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations, J. Comput. Appl. Math., 228 (2009) 296–303], the authors point out some flaws in the results of YoonMe Ham et al. and present some modified variants of the method. In this paper we point out that the paper of Liang Fang et al. itself contains some flaw results and we correct them by using symbolic computation in Mathematica. Moreover, we show that the main result in Theorem 3 of Liang Fang et al. is wrong. The order of convergence of the method is’nt 3m+2, but is 2m+4. We give the general expression of convergence error too.

A Variant of Newton Method with Eighth-Order Convergence for Solving Nonlinear Equations

2012 ◽  
Vol 490-495 ◽  
pp. 51-55
Author(s):  
Liang Fang
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Eighth Order ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a variant of Newton method with order of convergence eight for solving nonlinear equations. The method is free from second derivatives. It requires three evaluations of the functions and two evaluations of derivatives in each step. Therefore the efficiency index of the presented method is 1.5157 which is better than that of classical Newton’s method 1.4142. Some numerical experiments illustrate that the proposed method is more efficient and performs better than classical Newton's method.

scholarly journals On an new Open type variant of Newton´s method

2014 ◽  
Vol 10 (2) ◽  
pp. 21-31
Author(s):  
Manoj Kumar
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Open Type ◽  
Numerical Tests ◽  
Comparison Of The Results

Abstract The aim of the present paper is to introduce and investigate a new Open type variant of Newton's method for solving nonlinear equations. The order of convergence of the proposed method is three. In addition to numerical tests verifying the theory, a comparison of the results for the proposed method and some of the existing ones have also been given.

scholarly journals Two Higher Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 14 (1) ◽  
pp. 179-187
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Higher Order ◽  
Secant Method ◽  
Subject Classification ◽  
Numerical Examples ◽  
Ams Subject Classification

 The main purpose of this paper is to derive two higher order iterative methods for solving nonlinear equations as variants of Mir, Ayub and Rafiq method. These methods are free from higher order derivatives. We obtain these methods by amalgamating Mir, Ayub and Rafiq method with standard secant method and modified secant method given by Amat and Busquier. The order of convergence of new variants are four and six. Also, numerical examples are given to compare the performance of newly introduced methods with the similar existing methods. 2010 AMS Subject Classification: 65H05 Journal of the Institute of Engineering, 2018, 14(1): 179-187

scholarly journals Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Fiza Zafar ◽  
Nawab Hussain ◽  
Zirwah Fatimah ◽  
Athar Kharal
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Hermite Interpolation ◽  
Convergent Method ◽  
Basins Of Attractions

We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton’s method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.

scholarly journals A family of modified Newton iteration method for solving nonlinear algebraic equations

2017 ◽  
Vol 20 (K2) ◽  
pp. 34-41
Author(s):  
Luc Xuan Nghiem ◽  
Hieu Nhu Nguyen
Keyword(s):  
Iteration Method ◽  
Order Of Convergence ◽  
Approximate Solutions ◽  
Newton Iteration ◽  
Convergence Order ◽  
Correction Function ◽  
Algebraic Equations ◽  
Order Condition ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method

In this study, a modified Newton iteration version for solving nonlinear algebraic equations is formulated using a correction function derived from convergence order condition of iteration. If the second order of convergence is selected, we get a family of the modified Newton iteration method. Several forms of the correction function are proposed in checking the effectiveness and accuracy of the present iteration method. For illustration, approximate solutions of four examples of nonlinear algebraic equations are obtained and then compared with those obtained from the classical Newton iteration method.

scholarly journals Multipoint Fractional Iterative Methods with (2α + 1)th-Order of Convergence for Solving Nonlinear Problems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 452
Author(s):  
Giro Candelario ◽  
Alicia Cordero ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Fractional Derivatives ◽  
Order Of Convergence ◽  
Recent Literature ◽  
Nonlinear Problems ◽  
Type Method ◽  
Numerical Tests ◽  
Multipoint Method

In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper, we introduce a new fractional Newton-type method with order of convergence α + 1 and compare it with the existing fractional Newton method with order 2 α . Moreover, we also introduce a multipoint fractional Traub-type method with order 2 α + 1 and compare its performance with that of its first step. Some numerical tests and analysis of the dependence on the initial estimations are made for each case, including a comparison with classical Newton ( α = 1 of the first step of the class) and classical Traub’s scheme ( α = 1 of fractional proposed multipoint method). In this comparison, some cases are found where classical Newton and Traub’s methods do not converge and the proposed methods do, among other advantages.

A Fixed-Point Iteration Method With Quadratic Convergence

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
K. P. Walker ◽  
T.-L. Sham
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unit Root ◽  
Iteration Method ◽  
Equation System ◽  
Higher Order ◽  
Iteration Algorithm ◽  
System Of Nonlinear Equations ◽  
Fixed Point Iteration ◽  
Root Functions

The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

Sign in / Sign up

Export Citation Format

Share Document